On union and intersection of type-2 fuzzy sets not expressible by the sup-t-norm extension principle

Xinxing Wu; Guanrong Chen; Lidong Wang

doi:10.1016/j.fss.2021.10.001

On union and intersection of type-2 fuzzy sets not expressible by the sup-t-norm extension principle

Xinxing Wu^*, Guanrong Chen, Lidong Wang^*

^*Corresponding author for this work

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

9 Citations (Scopus)

Abstract

This paper constructs a conjunction and a disjunction operator for type-2 fuzzy sets that cannot be expressed by the sup-t-norm extension principle applied to conjunction and disjunction of type-1 fuzzy sets by means of t-norms and t-conorms on the unit interval. This result answers affirmatively an open problem posed by Hernández et al. in 2015. The duality between the set-theoretic operators for type-2 fuzzy sets is obtained from the duality of set-theoretic operations on type-1 fuzzy sets.

Original language	English
Pages (from-to)	241-261
Journal	Fuzzy Sets and Systems
Volume	441
Online published	7 Oct 2021
DOIs	https://doi.org/10.1016/j.fss.2021.10.001
Publication status	Published - 5 Aug 2022

Research Keywords

Normal and convex function
t-Conorm
t-Norm
Type-2 fuzzy set

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title = "On union and intersection of type-2 fuzzy sets not expressible by the sup-t-norm extension principle",

abstract = "This paper constructs a conjunction and a disjunction operator for type-2 fuzzy sets that cannot be expressed by the sup-t-norm extension principle applied to conjunction and disjunction of type-1 fuzzy sets by means of t-norms and t-conorms on the unit interval. This result answers affirmatively an open problem posed by Hern{\'a}ndez et al. in 2015. The duality between the set-theoretic operators for type-2 fuzzy sets is obtained from the duality of set-theoretic operations on type-1 fuzzy sets.",

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author = "Xinxing Wu and Guanrong Chen and Lidong Wang",

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doi = "10.1016/j.fss.2021.10.001",

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T1 - On union and intersection of type-2 fuzzy sets not expressible by the sup-t-norm extension principle

AU - Wu, Xinxing

AU - Chen, Guanrong

AU - Wang, Lidong

PY - 2022/8/5

Y1 - 2022/8/5

N2 - This paper constructs a conjunction and a disjunction operator for type-2 fuzzy sets that cannot be expressed by the sup-t-norm extension principle applied to conjunction and disjunction of type-1 fuzzy sets by means of t-norms and t-conorms on the unit interval. This result answers affirmatively an open problem posed by Hernández et al. in 2015. The duality between the set-theoretic operators for type-2 fuzzy sets is obtained from the duality of set-theoretic operations on type-1 fuzzy sets.

AB - This paper constructs a conjunction and a disjunction operator for type-2 fuzzy sets that cannot be expressed by the sup-t-norm extension principle applied to conjunction and disjunction of type-1 fuzzy sets by means of t-norms and t-conorms on the unit interval. This result answers affirmatively an open problem posed by Hernández et al. in 2015. The duality between the set-theoretic operators for type-2 fuzzy sets is obtained from the duality of set-theoretic operations on type-1 fuzzy sets.

KW - Normal and convex function

KW - t-Conorm

KW - t-Norm

KW - Type-2 fuzzy set

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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85117854735&origin=recordpage

U2 - 10.1016/j.fss.2021.10.001

DO - 10.1016/j.fss.2021.10.001

M3 - RGC 21 - Publication in refereed journal

SN - 0165-0114

VL - 441

SP - 241

EP - 261

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

ER -

On union and intersection of type-2 fuzzy sets not expressible by the sup-t-norm extension principle

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Research Keywords

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